Question

The relationship between average acceleration a, change in velocity Δυ, and the amount of time passed t is as follows:

a= t/Δυ
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Over a constant time period (t), a cat had a higher average acceleration than a dog. What must be true?
a) The change in velocity (Δυ) of the cat is greater than that of the dog.
b) The time passed (t) for the cat is greater than that for the dog.
c) The change in velocity (Δυ) of the cat is less than that of the dog.
d) The time passed (t) for the cat is less than that for the dog.

Answer 1

The correct answer is a) The change in velocity (Δυ) of the cat is greater than that of the dog. This is due to the proportionality of average acceleration to change in velocity when time is constant.

Step-by-step explanation:

The question concerns the relationship between average acceleration, change in velocity (Δυ), and the amount of time passed (t), with the formula given as a = Δυ/t. If a cat has had a higher average acceleration than a dog over a constant time period (t), then it is necessary that the cat had to undergo a greater change in velocity (Δυ) than the dog during this time period. Given that the time t remained constant for both the cat and dog, the only way for the cat to achieve a higher acceleration is if its change in velocity was larger. Therefore, the correct answer is:

a) The change in velocity (Δυ) of the cat is greater than that of the dog.

This is because average acceleration is directly proportional to the change in velocity when time is held constant. A greater change in velocity (Δυ) over the same time period (t) would lead to greater acceleration (a).